Question

True or false if the dimensions of a cylinder are doubled then its volume is quadrupled.

Answer 1

VOLUME OF A CYLINDER = pi X r X r X h 

pi X 2r X 2r X 2h = 8pir^2h 

Volume is 8 times 

ANSWER IS FALSE

Answer 2

Answer:  The given statement is FALSE.

Step-by-step explanation:  We are given to check whether the following statement is true or false :

"If the dimensions of a cylinder are doubled then its volume is quadrupled."

We know that

the volume of a cylinder with radius r units and height h units is given by

$V=\pi r^2h.$

If the dimensions are doubled, then the new dimensions will be

R = 2r  and  H = 2h.

Therefore, the new volume will be

$V'=\pi R^2H=\pi \times(2r)^2\times (2h)=8\times \pi r^2 h=8V.$

Thus, the volume of the new cylinder will be 8 times the original one, not quadrupled.

So, the given statement is FALSE.